27/20: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Pailiaq (talk | contribs)
mNo edit summary
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
Line 7: Line 7:
In [[5-limit]] [[just intonation]], '''27/20''', the '''classic acute fourth''', is an interval measuring about 519.6{{cent}}. It differs from the [[4/3]] perfect fourth by [[81/80]] (about 21.5{{cent}}), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3/2]] perfect fifths, or as the interval between [[10/9]] and [[3/2]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as [[5/4]] and [[9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.
In [[5-limit]] [[just intonation]], '''27/20''', the '''classic acute fourth''', is an interval measuring about 519.6{{cent}}. It differs from the [[4/3]] perfect fourth by [[81/80]] (about 21.5{{cent}}), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3/2]] perfect fifths, or as the interval between [[10/9]] and [[3/2]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as [[5/4]] and [[9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.
== Approximation ==
== Approximation ==
{{Interval_Edo_Approximation | 27/20}
{{Interval edo approximation|27/20}
== See also ==  
== See also ==  
* [[40/27]] – its [[octave complement]]
* [[40/27]] – its [[octave complement]]

Revision as of 13:06, 3 November 2025

Interval information
Ratio 27/20
Factorization 2-2 × 33 × 5-1
Monzo [-2 3 -1
Size in cents 519.5513¢
Names wolf fourth,
classic acute fourth
Color name g4, gu 4th
FJS name [math]\displaystyle{ \text{P4}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.07682
Weil norm (log2 max(n, d)) 9.50978
Wilson norm (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc

In 5-limit just intonation, 27/20, the classic acute fourth, is an interval measuring about 519.6 ¢. It differs from the 4/3 perfect fourth by 81/80 (about 21.5 ¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five 3/2 perfect fifths, or as the interval between 10/9 and 3/2. In 12edo and meantone systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as 5/4 and 9/8. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.

Approximation

{{Interval edo approximation|27/20}

See also